Here, \(g(\overline{c})\)  and \(f(\phi )\) 
describe the homogeneous energy contributions from the Cahn-Hilliard
and PFC equations respectively. The composition gradient-energy coefficient
is given by \(\kappa \) . The operator \(G(\nabla _{c}^{2})\)  controls
the coarse-grained lattice symmetry described by the particle density
field. This operator is modeled as a function of the composition field
and is discussed in detail later on in this section. The coefficients,
\(F_{0}\)  and \((\overline{c}_{a},\overline{c}_{b})\) , correspond to
the energy barrier height and to the local equilibrium states of \(g(\overline{c})\) 
respectively. The parameter \(a\Delta T\)  , controls the second-order
phase transition of the PFC model. In this paper, we model \(a\Delta T\) 
as a constant to always describe a crystalline-solid state. The parameters
\(\lambda ,q_{0},u\) , relate the PFC equation to the first-order peak
in an experimental structure factor. Further details on these coefficients
are explained in the work by Elder and Grant [1]}. 
